Bao Le Hung (IAS)
Towards algebraic models for certain potentially crystalline deformation rings

Abstract: The geometry of local Galois deformation rings with p-adic Hodge theoretic conditions play a central role in many arithmetic questions, such as the weight part of Serre's conjecture and modularity lifting theorems, yet they remain poorly understood in most situations. I will describe a finite type variety whose formal completions are conjecturally describing certain such deformation rings and explain an avatar of the geometric Breuil-Mezard conjecture on this model. This is joint work with D. Le, B. Levin and S. Morra.